Substitution Dynamical Systems: Characterization of Linear Repetitivity and Applications

Details Substitution Dynamical Systems: Characterization of Linear Repetitivity and Applications Substitution Dynamical Systems: Characterization of Linear Repetitivity and Applications

2003-02-19

arxiv.org/abs/math/0302231v2

Mathematics

Dynamical Systems

14 pages, assumption (4) included

Scientific paper

We consider dynamical systems arising from substitutions over a finite
alphabet. We prove that such a system is linearly repetitive if and only if it
is minimal. Based on this characterization we extend various results from
primitive substitutions to minimal substitutions. This includes applications to
random Schr\"odinger operators and to number theory.

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